Fibers have played a critical role in the long history of human development. They are the basic building blocks of textiles. Synthetic fibers not only make clothes stronger and more durable, but are also customizable and cheaper. The growth of miniature and wearable electronics has promoted the development of smart and multifunctional fibers. Particularly, the incorporation of functional semiconductors and electroactive materials in fibers has opened up the field of fiber electronics. The energy supply system is the key branch for fiber electronics. Herein, after a brief introduction on the history of smart and functional fibers, we review the current state of advanced functional fibers for their application in energy conversion and storage, focusing on nanogenerators, solar cells, supercapacitors and batteries. Subsequently, the importance of the integration of fiber-shaped energy conversion and storage devices via smart structure design is discussed. Finally, the challenges and future direction in this field are highlighted. Through this review, we hope to inspire scientists with different research backgrounds to enter this multi-disciplinary field to promote its prosperity and development and usher in a truly new era of smart fibers.